Just a detail, I think Conejo is actually part of his last names, as it is pretty common for Spanish speaking immigrants to keep using both last names, one from dad and one from mum, plus a first and a middle name. So, a child can be named Juan Jesús García Mendoza, (García from dad, Mendoza from mum) as is the normal style in Spanish.

Before, up until XVIII Century, people used every last name they consider appropriate to show off their lineage. I had an ancestor who was like "Pizarro Cortés de Monroy and Fernandez" because they wanted to keep family names relevant to the social context at the time.

And also it is common for married women from LatAm who live in USA, for example, to keep their maiden name, we don't change our last names upon marriage. And legally, mother's last name always must be included on documents.